How do I change the default output file format and location
You can set the settings however you like and then press Ctrl+U to save de default blender scene.

Next time you open blender or start a new project your saved preferences will be as you like.



And yes, there is a good reason why you want to render as images first and then encode as video later:


If you render as video and something goes wrong you will have to start over, as opposed as having to render only the missing frames on an image sequence.
Rendering directly as video can tie up your machine for a very long time, with no real way to stop and re-start the render process.
Other reason to use image sequences is that you can then experiment with different video encoding settings, and compression schemes, and data rates without having to start from scratch.


Render directly to video only to assess the progress, pacing and problems with the animation project, rendering a small or low res as a video file will allow you to evaluate animations in real time.



As for the .png being the default format... well... there is an interesting discussion on this link:

Why is the default image format for saving renders is in PNG?